Answer
The water balloon will NOT hit her. It will come close by $1-0.819=0.181m$ at the height level of her head.
Work Step by Step
Height for the water balloon to travel $= 18-1.7=16.3m$
$S=ut+\frac{1}{2}gt^{2}$
So, $16.3=0+0.5\times 9.8\times t^{2}$
$t=1.82s$
So, in 1.82s, the professor will move $=1.82\times 0.45=0.819m$ which is less than 1m.
So, the water balloon will NOT hit her. It will come close by $1-0.819=0.181m$ at the height level of her head.
